The TC loses light because it changes the optical characteristic of the lens
Yes. now think about what those optical characteristics are that it changes.
The TC is attached to the back of the lens. The light coming out the back of the lens and entering the TC is exactly the same as the light would be if there was no TC attached.
Now consider a ray of light that would end up just a little bit inside the edge of the frame if there was no TC. Does that light reach the frame if the TC is attached? No. The TC spreads the light coming from the lens over a wider image circle than the lens does without the TC. What happens when you spread the same amount of light over a larger area? You get a lower exposure.
The sensor size is the same.
Yes, but the angle of the cone of light cast by the Lens+TC is larger than that cast by the lens alone. The same amount of light passed through the lens, but it was spread over a wider area. Some of the light that went into the lens and came out at the other end that would have hit the sensor without the TC being present, doesn't hit the sensor when the TC is present. With the TC, more of the light passing through the lens was spread outside of that same-sized sensor. What happens to the density of something when you spread the same amount of it over a larger area? The density of it decreases. What happens to the density of a substance over a specific area when you spread less of the substance over that area? The density deceases. So with a TC, the exposure (the density of light on the sensor plane) is reduced because the TC spreads the same amount of light over a larger area, and spreads less of the light over the sensor.
With a TC you are simply using a lens with a longer FL and smaller aperture.
No, the physical aperture diameter has not changed. There has been no narrowing of aperture to reduce the amount of light getting through the lens. The same amount of light comes through the lens. But that light is spread out more by the TC.
What has changed is the f-number. An f-number is simply a constant divided into the effective focal length of a lens such that the division gives the physical diameter of the entrance pupil. You change the f-number of a lens either by changing the physical diameter of the lens aperture or by changing the focal length of the lens. Changing the physical diameter of the lens aperture changes the amount of light passing through the lens. Changing the focal length changes, does not change the amount of light passing through the lens, It changes how wide an area over the light is spread over. Both of these change the density of light falling on the sensor- they change the exposure.
Are you denying that the TC spreads the light coming from the lens wider than the lens alone spreads it?
- If you deny that the TC spreads the light, explain why light from a point in the scene near the edge of the scene shows up in the image frame when the TC is not attached but does not show in the image frame when the TC is attached.
- If you do not deny that the TC spreads the light coming from the lens, how do you maintain that the spreading is not what causes the reduction in exposure?
Saying that the exposure changes because the addition of the TC changes the f-number is just magical hand-waving. I'm explaining the mechanism of
how the TC works, and why how it works results in a narrower field of view and a lower exposure.
from, say, F4.0 to F5.6 by physically adding a further element.
Adding an element does not change the amount of light coming through the lens. The f-number changes because the focal length changed and the aperture diameter stayed the same. So how did the addition of the TC change the focal length? It did so by spreading out the light coming through the lens more than it would have spread if the TC wasn't attached. So the field of view on the sensor is narrower with the TC than without. The spreading of the light is the mechanism that the TC uses to narrow the angle of view on the sensor (increase the focal length) and that results in a loss of exposure.
You have to expose for a 5.6 lens which is 1 stop more.
Yes, because the spreading of the light by the TC reduced the density of light on the sensor by 1/2.
The additional noise seen after cropping is nothing to do with light, but simply that the noise is seen more easily with greater magnification.
Cropping and viewing does not involve magnification. It involves enlargement. Enlarging an image doesn't change its SNR. However, the SNR of the cropped area is actually lower than the SNR of the image from which it was cropped.
The issue is whether the image degradation as a result of adding a TC and having to use a higher iso is more or less than that from resizing and interpolation.
A higher ISO doesn't cause more noise. Lower exposure does.
Of course that's right and barely needs saying. However with a lens with smaller aperture (which is what a lens with TC attached is)
No. The lens with TC doesn't have a smaller aperture. Its aperture has not changed in size. The f-number changed because the aperture remained the same size but the angle of view on the sensor narrowed = the focal length increased. Since the aperture diameter didn't change, the amount of light passing through the lens did not change.
is going to lead to lower exposure,
The lower exposure, which is a lower density of light on the sensor, is caused by the TC spreading the same amount of light over a wider area, with more of that light falling outside the sensor. Only half the light that fell on the sensor before the TC was attached falls on the sensor after the TC is attached, yet the same amount of light passed though the lens in both cases.
which has to be compensated by slower shutter speed or corrected after exposure by using higher iso. If aperture is fixed, there has to be a compromise between slower exposure and potential movement blur, or lower exposure and lightness compensation (done by higher iso or PP exposure adjustment) Without going in to the details, allowing the iso to rise to get in to the higher 'in camera' range, and then PP seems to serve me best. Do you disagree?
I'd say widening the aperture would be best, followed by increasing ISO if you can't widen the aperture, with lightening in development as least desirable. But I also think this discussion of how to handle the decrease in exposure caused by the addition of a TC is off-topic.
So there is some degradation from using the TC, both optical and as a result of the lower exposure.
Yes. I have always agreed that the use of TC decreases maximum possible exposure. I just explained how the TC causes the reduction in exposure and for some unfathomable reason, you disagreed with my explanation of the mechanism, without suggesting a different mechanism.
There is some degradation from upressing as well,
In terms of SNR the amount of degradation is the same . In terms of sharpness, I have insufficient information to comment, other than to point out that interpolation, which is the mechanism Gigapixel must use, is inherently less likely to be accurate than magnification.
I am simply asking for demonstrable evidence which shows which approach is best.
I can only give you the physics foundation. I don't use Gigapixel, and I don't have the lens and TC you are interested in (I do have and use a TC).